Question: What do the following two equations represent? $-x+3y = -3$ $-3x-y = 5$
Answer: Putting the first equation in $y = mx + b$ form gives: $-x+3y = -3$ $3y = x-3$ $y = \dfrac{1}{3}x - 1$ Putting the second equation in $y = mx + b$ form gives: $-3x-y = 5$ $-y = 3x+5$ $y = -3x - 5$ The slopes are negative inverses of each other, so the lines are perpendicular.